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. 2024 Jan 3;625(7993):66–73. doi: 10.1038/s41586-023-06786-y

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — DEED balances the entropy gains with enthalpy costs for forming a single-phase, predicting synthesizability. a,b, Here its superior performance is compared with EFA and VEC for carbides (a) and carbonitrides (b), and represent systems forming single- and multiphases, respectively. The references for the previous experimental results are listed in Table 1. Our validation experiments presented in this paper are set in bold. The misclassification regions, in grey, encompass all single-phase systems that are on the incorrect side of the single- and/or multiphase threshold (vertical line). c, The XRD spectra for carbonitrides. The five green spectra show single-phase FCC systems, whereas the four red lines reveal extra peaks related to the WC hexagonal phase. d, Microstructures from SEM analysis for the nine compounds and three magnified regions of (HfMoNbTaW)CN showing the lamellar ‘pearlite-like’ microstructures and their principle wavelength λ_p. a.u., arbitrary units. Scale bar, 10 μm.

Inline graphic — DEED balances the entropy gains with enthalpy costs for forming a single-phase, predicting synthesizability. a,b, Here its superior performance is compared with EFA and VEC for carbides (a) and carbonitrides (b), and represent systems forming single- and multiphases, respectively. The references for the previous experimental results are listed in Table 1. Our validation experiments presented in this paper are set in bold. The misclassification regions, in grey, encompass all single-phase systems that are on the incorrect side of the single- and/or multiphase threshold (vertical line). c, The XRD spectra for carbonitrides. The five green spectra show single-phase FCC systems, whereas the four red lines reveal extra peaks related to the WC hexagonal phase. d, Microstructures from SEM analysis for the nine compounds and three magnified regions of (HfMoNbTaW)CN showing the lamellar ‘pearlite-like’ microstructures and their principle wavelength λ_p. a.u., arbitrary units. Scale bar, 10 μm.